Bauhaus-Universität Weimar

On sound and atmospheric vibrations, with the mathematical elements of music
Airy, George Biddell
(more conspicuous in approaching to unison than in 
approaching to the other concords), which finally disap¬ 
pears, leaving a most agreeable and animating concord. 
The sound which then reaches the ear is not like a 
simple note, but it gives no idea of two sounds; although 
when compared with either of the original notes, as 
sounded on a third string, it seems to be related to 
89. Mechanical explanation of Concords of Har¬ 
With our knowledge that every musical note implies 
a series of vibrations of air, following with similarity 
of character and at equal intervals of time (Article 71), 
the explanation of all these observed facts is simple. 
For instance, to explain the harmony in the coexistence 
of two sounds separated by an octave. Geometrically, 
we may represent the disturbance of the air produced 
by the lower sound as a series of waves of a certain 
length travelling with sound-velocity ; and the disturb¬ 
ance produced by the upper sound as a series of waves of 
half the length travelling with the same sound-velocity, 
and therefore always holding the same relation to the 
series of longer waves. The union of these produces 
a wave more complex than either separately. If the 
long wave be much the larger, (in the amplitude of 
vibrations of its particles,) the result will be a modi¬ 
fied long wave, or (musically) a modified low note; 
if the short wave be much the larger, the result will be


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